(Answered)-A Niskanian bureaucracy supplies some output Q at the following - (2025 Updated Original AI-Free Solution

Question

1. A Niskanian bureaucracy supplies some output Q at the following cost: TC = 1.5Q^2 where costs are measured in tens of millions of dollars.
   1. a) ?If the legislature?s willingness-to-pay curve is B = 8Q ? 2Q^2, what is the maximum budget that the bureau can secure? Be sure to consider both demand and cost constraints. (4 points)
   2. b) ?Now the legislature institutes the following monitoring scheme: With probability p the bureaucracy is audited (which would reveal that the optimal level of production from the legislature?s point of view is Q0 = 1.2). If the bureaucracy is caught producing more than Q0 it is forced to pay a fine of f * (Q ? Q^0) = f * (Q ? 1.2), which is measured in the same units as production costs. Write out an expression for the bureau?s expected total costs when it produces less than or equal to Q0, and for when it produces more than Q0. (2 points)
   3. c) ?If p = 0.2 and f = 5, how much will the bureau produce? (4 points)
   4. d) ?Bonus (4 points): What about if p = 0.5 and f = 10? Illustrate the intuition behind these answers.

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